Data cells of plural classes are transferred from input ports to output ports through a switch by storing the cells at each input port in class-specific virtual output queues (VOQ) within sets of VOQs associated with output ports, and providing credits to VOQs according to class-associated guaranteed bandwidths. When a cell is received at a VOQ having credits, a high-priority request for transfer is generated. If a cell is received at a VOQ that does not have any available credits, a low-priority request for transfer is generated. In response to requests, grants are issued to VOQ sets without regard to class, high-priority requests being favored over low-priority requests. When a grant is received for a particular VOQ set, an arbitrator selects a VOQ from the set, giving priority to VOQs having credits over VOQs without credits, and a cell from the selected VOQ is transferred. Requests generated from all input ports are forwarded to a central scheduler associated with a switch fabric slice, the central scheduler issuing the grants. The switch fabric may comprise multiple slices and a central scheduler, across which requests may be distributed in parallel, for example, the switch fabric slices being selected in a fixed order. While all high-priority requests are granted, low priority requests may be granted by the central scheduler according to a weighted fair share policy.